I'm not sure it's fair to refer to them as "cults" - at least, unless you're the sort that maintains that ANY religion is a cult, and the established religions are just cults that have gone mainstream. Worship of the Twelve is perfectly acceptable in Eorzea, even expected, to a degree - whereas true cults, like the Lambs of Dalamud, are looked upon as delusional and (justifiably) dangerous fanatics.

In-game, however, I think that Ishgard's worship of Halone is the only case whose worship is gone into in with any depth, and appears to be patterned after Catholicism (specifically, medieval, Inquisition-era Catholicism). It's worth noting, however, that worshipers of Halone never downplayed any of the other Eleven as being "false gods" - while Halone is the center of their worship, the others are no less godly than she. Even Nophica, Halone's bitter rival, is never singled out as being unworthy of worship. Also worth noting, it may well be the case that non-Ishgardian worshipers of Halone do not subscribe to Ishgard's church, but worship her in their own way.

It's also risky to generalize that Au Ra do not worship the Twelve. The Twelve are worshiped in Eorzea, and while most Au Ra do not live in Eorzea, the few that are born and bred there probably DO. Worship of the Twelve is a regional and cultural thing, not a racial thing.